Deck 14: Oscillations

Question 1

A mass m hanging on a spring with a spring constant k executes simple harmonic motion with a period T.If the same mass is hung from a spring with a spring constant of 2k,the period of oscillation

A)increases by a factor of 2.
B)decreases by a factor of 2.
C)increases by a factor of .
D)decreases by a factor of .
E)is not affected.

Answer 1

decreases by a factor of .

Question 2

A body of mass 5.0 kg moves in simple harmonic motion according to the equation where the units are SI.The period of this motion is

A)1/30 s
B) $\pi$ /15 s
C) $\pi$ /6 s
D)15/ $\pi$ s
E)30 s

Answer 2

$\pi$ /15 s

Question 3

The frequency of a simple harmonic motion is 2.6 $\times$ 10^-4 s^-1.The oscillation starts (t = 0)when the displacement has its maximum positive value of 6.5 $\times$ 10^-3 cm.The earliest possible time at which the particle can be found at x = -2.6 $\times$ 10^-3 cm is

A)7.1 $\times$ 10^-6 s
B)1.2 $\times$ 10^-5 s
C)1.1 $\times$ 10^-4 s
D)1.1 $\times$ 10^-3 s
E)4.2 $\times$ 10^-3 s

Answer 3

1.2 $\times$ 10^-5 s

Question 4

A particle is oscillating with simple harmonic motion.The frequency of the motion is 10 Hz and the amplitude of the motion is 5.0 cm.As the particle passes its central equilibrium position,the acceleration of the particle is

A)100 cm/s²
B)1.6 $\times$ 10⁵ cm/s²
C)4 $\times$ 10⁶ cm/s²
D)zero
E)3.2 $\times$ 10⁶ cm/s²

Question 5

When an object is oscillating in simple harmonic motion in the vertical direction,its maximum speed occurs when the object

A)is at its highest point.
B)is at its lowest point.
C)is at the equilibrium point.
D)has the maximum net force exerted on it.
E)has a position equal to its amplitude.

Question 6

A particle with a mass of 65 g is moving with simple harmonic motion.At time t = 0,the particle is at its extreme positive displacement of 18.0 cm.The period of the motion is 0.600 s.At time t = 1.35 s,the velocity of the particle is

A)-1.9 m/s
B)zero
C)0.84 m/s
D)+1.9 m/s
E)-0.84 m/s

Question 7

If F is the force,x the displacement,and k a particular constant,for simple harmonic motion we must have

A)F = -k/x²
B)F = k/x
C)F = (k/x²)^1/2
D)F = -kx²
E)None of these is correct.

Question 8

A spring vibrates in simple harmonic motion according to the equation where x is in centimeters and t is in seconds.The total number of vibrations this body makes in 10 s is

A)0.5
B)10
C) $\pi$
D)15
E)5

Question 9

You want a mass that,when hung on the end of a spring,oscillates with a period of 1 s.If the spring has a spring constant of 10 N/m,the mass should be

A)10 kg
B) kg
C)4 $\pi$ ²(10)kg
D)10/(4 $\pi$ ²)kg
E)None of these is correct.

Question 10

A particle moving with a simple harmonic motion has its maximum displacement of +18 cm at time t = 0.The frequency of the motion is 10 s^-1.At a time t = 0.65 s,the position of the particle is

A)+18 cm
B)zero
C)-13 cm
D)-18 cm
E)+7.3 cm

Question 11

A particle moving with simple harmonic motion has a maximum displacement of +12.0 cm.The particle moves from its maximum positive to its maximum negative displacement in 2.25 s.The motion starts when the displacement is x = +12.0 cm.The time for the particle to move to x = -6.00 cm is

A)1.70 s
B)0.750 s
C)1.50 s
D)2.20 s
E)0.983 s

Question 12

The equation for the period T of a mass m oscillating with simple harmonic motion at the end of a spring with a force constant k is .A mass m that is oscillating on a spring with a force constant of 0.52 N/m has a period of 2.1 s.On a second spring,the same mass has a period of 3.5 s.The force constant of the second spring is

A)impossible to determine because the mass is not given.
B)0.19 N/m
C)1.4 N/m
D)0.31 N/m
E)0.75 N/m

Question 13

The instantaneous speed of a mass undergoing simple harmonic motion on the end of a spring depends on

A)the amplitude of oscillation.
B)the frequency of oscillation.
C)the period of oscillation.
D)the time at which the speed is measured.
E)all of these

Question 14

Any body moving with simple harmonic motion is being acted on by a force that is

A)constant.
B)proportional to a sine or cosine function of the displacement.
C)proportional to the inverse square of the displacement.
D)directly proportional to the displacement.
E)proportional to the square of the displacement.

Question 15

A mass m hanging on a spring with a spring constant k has simple harmonic motion with a period T.If the mass is doubled to 2m,the period of oscillation

A)increases by a factor of 2.
B)decreases by a factor of 2.
C)increases by a factor of
D)decreases by a factor of
E)is not affected.

Question 16

A body moves with simple harmonic motion according to the equation where the units are SI.At t = 2 s,the speed of the body is

A)1/3 m/s
B)1/ $\pi$ m/s
C) m/s
D)4 m/s
E) m/s

Question 17

The force constant of a massless spring is 25.0 N/m.A mass of 0.45 kg is oscillating in simple harmonic motion at the end of the spring with an amplitude of 0.32 m.The maximum speed of the mass is

A)5.7 m/s
B)56 m/s
C)7.4 m/s
D)2.4 m/s
E)10 m/s

Question 18

A body oscillates with simple harmonic motion according to the equation where the units are SI.The speed of the body when it has a displacement of 3 m is

A) m/s
B)6 $\pi$ m/s
C)9 $\pi$ m/s
D) m/s
E)18 $\pi$ m/s

Question 19

A 2.00-kg body is attached to a spring of negligible mass and oscillates with a period of 1.00 s.The force constant of the spring is

A)0.051 N/m
B)0.500 N/m
C)2.00 N/m
D)6.28 N/m
E)None of these is correct.

Question 20

A particle moving in simple harmonic motion with a period T = 1.5 s passes through the equilibrium point at time t₀ = 0 with a velocity of 1.00 m/s to the right.A time t later,the particle is observed to move to the left with a velocity of 0.50 m/s.(Note the change in direction of the velocity.)The smallest possible value of the time t is

A)0.17 s
B)0.33 s
C)0.50 s
D)0.25 s
E)0.82 s

Question 21

A body of mass 0.50 kg moves in simple harmonic motion with a period of 1.5 s and an amplitude of 20 mm.Which of the following equations correctly represents this motion?

A)x = 40 cos(t/1.5)mm
B)x = 40 cos(2 $\pi$ t/1.5)mm
C)x = 20 sin(t/1.5)mm
D)x = 20 sin(1.5 $\pi$ t)mm
E)x = 20 sin(2 $\pi$ t/1.5)mm

Question 22

A body of mass M is executing simple harmonic motion with an amplitude of 8.0 cm and a maximum acceleration of 100 cm/s².When the displacement of this body from the equilibrium position is 6.0 cm,the magnitude of the acceleration is approximately

A)8.7 cm/s²
B)21 cm/s²
C)35 cm/s²
D)17 cm/s²
E)1.3 m/s²

Question 23

The equation of a body in simple harmonic motion is where y is in centimeters and t is in seconds.The frequency of the oscillations is

A) $\pi$ /10 Hz
B) $\pi$ /4 Hz
C)10/ $\pi$ Hz
D)8 Hz
E)20 Hz

Question 24

In simple harmonic motion,the displacement x = A cos $\omega$ t and the acceleration a = - $\omega$ ²x.If A = 0.25 m and the period is 0.32 s,the acceleration when t = 0.12 s is

A)zero
B)+3.9 m/s²
C)-3.9 m/s²
D)+6.8 m/s²
E)-6.8 m/s²

Question 25

Use the following to answer the question:

-The object in the diagram is in circular motion with frequency f.At t = 0 it was at (A,0).The y component of its acceleration is given by

A)a_y = (v_y - v_0y)/t
B)a_y = -(2 $\pi$ f)²A cos 2 $\pi$ ft
C)a_y = -(2 $\pi$ )²A sin 2 $\pi$ t
D)a_y = -(2 $\pi$ f)²A sin 2 $\pi$ ft
E)a_y = -(2 $\pi$ )²A cos 2 $\pi$ t

Question 26

In the following equations,a is acceleration,r is a fixed distance,s is displacement,and m is mass.Which equation describes simple harmonic motion?

A)a = -kr²
B)a = $\pi$ r²
C)a = -ks^-1
D)a = 4 $\pi$ mr²/3
E)a = - 4 $\pi$ ms/3

Question 27

A particle moving in a circle of radius 15 cm makes 33.3 rev/min.If the particle starts on the positive x axis at time t = 0,what is the x component of the particle's velocity at time t = 1.2 s?

A)45 cm/s
B)-3.8 cm/s
C)26 cm/s
D)-45 cm/s
E)13 cm/s

Question 28

A body of mass 5.0 kg moves in simple harmonic motion according to the equation where the units are SI.The maximum speed of this body is approximately

A)0.013 m/s
B)0.40 m/s
C)0.60 m/s
D)1.2 m/s
E)30 m/s

Question 29

A ball moves back and forth in simple harmonic motion along a line 12 cm long.When the ball is 4 cm from the left-hand end of its path,it has an acceleration of 24 cm/s².When the ball is 1 cm from the right-hand end of its path the magnitude of its acceleration is

A)15 cm/s²
B)30 cm/s²
C)3 cm/s²
D)60 cm/s²
E)88 cm/s²

Question 30

Use the following to answer the question:

-The object in the diagram is in circular motion with frequency f.At t = 0 it was at (A,0).The y component of its velocity is given by

A)v_y2 = v_0y2 + 2a(y - y₀)
B)v_y = 2 $\pi$ fA cos 2 $\pi$ t
C)v_y = A sin ft
D)v_y = 2 $\pi$ fA sin 2 $\pi$ ft
E)v_y = A cos ft

Question 31

A body moves in simple harmonic motion with amplitude A and period T.The minimum time for the body to move from a displacement of A to A/2 is

A)T/2
B)T/4
C)T/6
D)T/12
E)T/16

Question 32

A light spring stretches 0.13 m when a 0.35 kg mass is hung from it.The mass is pulled down from this equilibrium position an additional 0.15 m and then released.Determine the maximum speed of the mass.

A)1.10 m/s
B)2.75 m/s
C)11.4 m/s
D)1.25 m/s
E)0.02 m/s

Question 33

An object is moving with simple harmonic motion.When the object is displaced 4 cm from its equilibrium point,its acceleration is 20 cm/s².Calculate the period T.

A)0.45 s
B)0.36 s
C)2.2 s
D)2.8 s
E)none of the above

Question 34

The top graph represents the variation of displacement with time for a particle executing simple harmonic motion.Which curve in the bottom graph represents the variation of acceleration with time for the same particle?

A)1
B)2
C)3
D)4
E)None of these is correct.

Question 35

A light spring stretches 0.13 m when a 0.35-kg mass is hung from it.The mass is pulled down from this equilibrium position an additional 0.12 m and is released.Determine the spring constant k and the amplitude of vibration.

A)26.4 N/m and 0.37 m
B)26.4 N/m and 0.12 m
C)2.70 N/m and 0.25 m
D)26.4 N/m and 0.25 m
E)26.4 N/m and 0.13 m

Question 36

A particle moves in one dimension with simple harmonic motion according to the equation where the units are SI.Its period is

A)4 $\pi$ ² s
B)2 $\pi$ s
C)1 s
D)1/(2 $\pi$ )s
E)1/(4 $\pi$ ²)s

Question 37

An object is moving with simple harmonic motion.When the object is displaced 5 cm from its equilibrium point,its velocity is 15.0 cm/s.Calculate the amplitude of motion if its period of motion is 3.0 s.

A)13.6 cm
B)7.1 cm
C)8.7 cm
D)5.0 cm
E)none of the above

Question 38

The acceleration of a particle moving with simple harmonic motion is given by where x is in meters and a is in meters per second squared.The period of the motion is

A)0.25 s
B)0.392 s
C)1.57 s
D)4.0 s
E)25.2 s

Question 39

A particle is moving with SHM.If it has velocities of v₁ and v₂ when it is at positions x₁ and x₂ from the equilibrium position respectively,then the square of the frequency of vibration (f ²)is given by:

A)(v₁² - v₂² )/ 4 $\pi$ ² (x₁² -x₂² )
B)(v₁² -v₂² )/ 4 $\pi$ ² (x₂² - x₁² )
C)(v₁² + v₂² )/ 4 $\pi$ ² (x₂² -x₁² )
D)(v₁² + v₂² )/ 2 $\pi$ ² (x₂² + x₁² )
E)(v₁² + v₂² )/ (x₂² - x₁² )

Question 40

Use the following to answer the question:

-The object in the diagram is in circular motion.Its position at t = 0 was (A,0).Its frequency is f.The y component of its position is given by

A)y = y₀ + v_0yt + at²
B)y = A cos 2 $\pi$ ft
C)y = A sin ft
D)y = A sin 2 $\pi$ ft
E)y = A cos ft

Question 41

A particle is moving with SHM.If it has velocities of 6 cm/s and 2 cm/s when it is at positions 4 cm and 7 cm respectively from the equilibrium position,then calculate its period of oscillation.

A)5.4 s
B)6.4 s
C)7.4 s
D)10.8 s
E)none of the above

Question 42

When the compression of a spring is doubled,the potential energy stored in the spring is

A)the same as before.
B)doubled.
C)tripled.
D)increased by a factor of 8.
E)None of these is correct.

Question 43

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface.
What is the rotational kinetic energy when the sphere is at the equilibrium position?

A)
B)
C)
D)
E)undetermined

Question 44

A simple way to test if a device can withstand high "g-force" is to attach the device to a vibrating platform.Suppose a device has to withstand up to 5g's,and the amplitude of the oscillation is 5 cm,the frequency of the vibration should be

A)5 Hz
B)981 Hz
C)31.3 Hz
D)44.3 Hz
E)62.6 Hz

Question 45

A 2.5-kg object is attached to a spring of force constant k = 4.5 kN/m.The spring is stretched 10 cm from equilibrium and released.What is the kinetic energy of the mass-spring system when the mass is 5.0 cm from its equilibrium position?

A)5.6 J
B)11 J
C)17 J
D)14 J
E)42 J

Question 46

The displacement in simple harmonic motion is a maximum when the

A)acceleration is zero.
B)velocity is a maximum.
C)velocity is zero.
D)kinetic energy is a maximum.
E)potential energy is a minimum.

Question 47

The energy of a simple harmonic oscillator could be doubled by increasing the amplitude by a factor of

A)0.7
B)1.0
C)1.4
D)2.0
E)4.0

Question 48

A system consists of a mass vibrating on the end of a spring.The total mechanical energy of this system

A)varies as a sine or cosine function.
B)is constant only when the mass is at maximum displacement.
C)is a maximum when the mass is at its equilibrium position only.
D)is constant,regardless of the displacement of the mass from the equilibrium position.
E)is always equal to the square of the amplitude.

Question 49

When the displacement of an object in simple harmonic motion is one-quarter of the amplitude A,the potential energy is what fraction of the total energy?

A)
B)
C)1/16
D)There is not enough information provided to answer correctly
E)None of these is correct.

Question 50

The force constant for a simple harmonic motion is k and the amplitude of the motion is A.The maximum value of the potential energy of a mass m oscillating with simple harmonic motion is

A)
B) kA²
C)kA²
D)kA
E)None of these is correct.

Question 51

If the amplitude of a simple harmonic oscillator is doubled,the total energy is

A)unchanged.
B)one-fourth as large.
C)half as large.
D)doubled.
E)quadrupled.

Question 52

In simple harmonic motion,the magnitude of the acceleration of a body is always directly proportional to its

A)displacement.
B)velocity.
C)mass.
D)potential energy.
E)kinetic energy.

Question 53

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface.
The angular frequency of the oscillation is

A)
B)
C)
D)
E)

Question 54

The displacement of a body moving with simple harmonic motion is given by the equation After one-quarter of a period has elapsed since t = 0,which of the following statements is correct?

A)Half the total energy of the body is kinetic energy and half is potential energy.
B)The kinetic energy is a maximum.
C)The potential energy is a maximum.
D)The total energy is a negative maximum.
E)Both kinetic and potential energies are maxima.

Question 55

A 2.50-kg object is attached to a spring of force constant k = 4.50 kN/m.The spring is stretched 10.0 cm from equilibrium and released.What is the maximum kinetic energy of this system?

A)45.0 J
B)22.5 J
C)56.0 J
D)2.25 $\times$ 10⁵ J
E)4.50 J

Question 56

A mass attached to a spring has simple harmonic motion with an amplitude of 4.0 cm.When the mass is 2.0 cm from the equilibrium position,what fraction of its total energy is potential energy?

A)one-quarter
B)one-third
C)one-half
D)two-thirds
E)three-quarters

Question 57

Which of the following statements is true of a particle that is moving in simple harmonic motion?

A)The momentum of the particle is constant.
B)The kinetic energy of the particle is constant.
C)The potential energy of Earth-particle system is constant.
D)The acceleration of the particle is constant.
E)The force the particle experiences is a negative restoring force.

Question 58

A body moving in simple harmonic motion has maximum acceleration when it has

A)maximum velocity.
B)maximum kinetic energy.
C)minimum potential energy.
D)minimum kinetic energy.
E)zero displacement.

Question 59

A mass on a spring oscillates with an amplitude of 5.0 cm.What is the position of the mass when the kinetic and potential energies are equal?

A)There is not enough information provided to answer this question.
B)1.2 cm
C)2.5 cm
D)3.5 cm
E)3.8 cm

Question 60

Use the figure to answer the next problem. A spring of negligible mass and spring constant k is attached to the wall on one end,and the other end is attached to the center of mass axis of a solid sphere of mass m and radius r.The spring is stretched a distance A from equilibrium and let go.The sphere rolls freely on a smooth surface.
What is the linear kinetic energy when the sphere is at the equilibrium position?

A)
B)
C)
D)
E)undetermined

Question 61

To double the period of a pendulum,the length

A)must be increased by a factor of 2.
B)must be decreased by a factor of 2.
C)must be increased by a factor of .
D)must be increased by a factor of 4.
E)need not be affected.

Question 62

The kinetic energy K of a body executing simple harmonic motion is plotted against time,the time being expressed in terms of the period T.The initial conditions are such that the phase angle is zero.Such a graph would most closely resemble which of the following graphs?

A)1
B)2
C)3
D)4
E)5

Question 63

If the length of a simple pendulum with a period T is reduced to half of its original value,the new period T is approximately

A)0.5T
B)0.7T
C)T (unchanged)
D)1.4T
E)2T

Question 64

A 1.0-kg mass oscillates along the x axis with simple harmonic motion.Its position as a function of time is given by where the units are SI.When t = 2 s,the kinetic energy of the mass is

A) $\pi$ ²/24 J
B) $\pi$ ²/72 J
C)2 $\pi$ ²/9 J
D)4 $\pi$ ²/9 J
E) $\pi$ ²/4 J

Question 65

The mass on the end of the spring (which stretches linearly)is in equilibrium as shown.It is pulled down so that the pointer is opposite the 11-cm mark and then released.The mass experiences its maximum upward velocity at which of the following positions?

A)3-cm mark
B)7-cm mark
C)1-cm mark
D)11-cm mark
E)None of these is correct.

Question 66

A 0.5-kg mass is suspended from a massless spring that has a force constant of 79 N/m.The mass is displaced 0.1m down from its equilibrium position and released.If the downward direction is negative,the displacement of the mass as a function of time is given by

A)y = 0.1 cos(158t - $\pi$ )
B)y = 0.2 cos(158t - $\pi$ )
C)y = 0.1 cos(12.6t - $\pi$ )
D)y = 0.2 cos(12.6t + $\pi$ )
E)y = 0.1 cos(2t + $\pi$ )

Question 67

A body of mass M suspended from a spring oscillates with a period T.If the mass of the spring can be neglected,a body of mass 2M,suspended from the same spring,oscillates with a period of

A)T/2
B)
C)T
D)
E)2T

Question 68

A Foucault pendulum is a simple mass-on-a-long-string pendulum suspended from a tall ceiling.It was first exhibited at the Pantheon building in Paris,and because of the rotation of Earth about its axis,the Pantheon rotates about the pendulum as the day passes.A similar pendulum set up at the North pole would show the floor below the pendulum rotating one circle in a 24hr period.If a Foucault pendulum is installed at the equator so that it originally swings in the east-west direction,after 6 hours what is the direction of the swing?

A)east-west
B)north-south
C)NE-SW
D)NW-SE
E)in any direction

Question 69

Both a mass-spring system and a simple pendulum have a period of 1 s.Both are taken to the moon in a lunar landing module.While they are inside the module on the surface of the moon,

A)the pendulum has a period longer than 1 s.
B)the mass-spring system has a period longer than 1 s.
C)both a and b are true.
D)the periods of both are unchanged.
E)one of them has a period shorter than 1 s.

Question 70

A rocket ship is propelled vertically up with an acceleration of g in a uniform gravitational field.A pendulum of length 1.0 m would have a period of

A)0
B)2.0 s
C)1.41 s
D)3.1 s
E)the period is infinite

Question 71

A 2-kg mass oscillates in one dimension with simple harmonic motion on the end of a massless spring on a horizontal frictionless table according to where the units are SI.The total mechanical energy of this system is

A)1 J
B)3 J
C)5 J
D)7 J
E)9 J

Question 72

A 1.81-kg block slides on a horizontal frictionless table with a speed of 1.22 m/s.It is brought to rest by compressing a spring in its path.If the spring has a force constant of 7.30 N/m,it is compressed

A)6.89 m
B)1.22 m
C)1.71 m
D)0.305 m
E)by none of these amounts

Question 73

A spring is cut in half.The ratio of the force constant of one of the halves to the force constant of the original spring is

A)
B)1
C)2
D)4
E)

Question 74

Two clocks with basic timekeeping mechanisms consisting of (1)a mass on a spring and (2)a simple pendulum are taken to the top of a mountain.At the base of the mountain,they both keep perfect time.At the top of the mountain,

A)neither keeps correct time.
B)only the pendulum clock keeps correct time.
C)only the mass-spring clock keeps correct time.
D)both keep correct time.
E)Not enough information is given to answer this question.

Question 75

An 8.0-kg block is attached to a spring with a constant of 2.0 N/m.If the spring is stretched 3.0 m from its equilibrium position and released from rest,the maximum velocity attained by the mass is

A)0.75 m/s
B)1.5 m/s
C)3.0 m/s
D)4.2 m/s
E)15 m/s

Question 76

A 0.10-kg mass stretches a massless spring 0.20 m from its equilibrium position.If this same mass is set into vibration on this spring,the frequency is

A)0.023 Hz
B)1.1 Hz
C)2.0 Hz
D)7.0 Hz
E)13 Hz

Question 77

A 10-kg block starts from rest at a vertical height of 1 m on a 30º frictionless inclined plane.If the block slides down the incline and then 20 m along a frictionless horizontal surface into a fixed spring with a force constant of 100 N/m,the spring is compressed approximately

A)1.4 m
B)2.0 m
C)0.33 m
D)0.98 m
E)2.5 m

Question 78

A 0.454-kg block starts from rest and slides 3.05 m down a frictionless plane inclined at 53º to the horizontal.At the bottom it slides 9.14 m over a horizontal frictionless plane before compressing a spring (k = 14.7 N/m)a distance x and coming momentarily to rest.The value of x is approximately

A)0.215 m
B)1.52 m
C)2.44 m
D)1.83 m
E)1.21 m

Question 79

A mass of 2.00 kg suspended from a spring 100 cm long is pulled down 4.00 cm from its equilibrium position and released.The amplitude of vibration of the resulting simple harmonic motion is

A)4.00 cm
B)2.00 cm
C)8.00 cm
D)1.04 cm
E)1.02 cm

Question 80

A clock keeps accurate time when the length of its simple pendulum is L.If the length of the pendulum is increased a small amount,which of the following is true?

A)The clock will run slow.
B)The clock will run fast.
C)The clock will continue to keep accurate time.
D)The answer cannot be determined without knowing the final length of the pendulum.
E)The answer cannot be determined without knowing the percentage increase in the length of the pendulum.